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= {(x, y) E R´ | x = y}U{(x, y) E R² |x = -2y}. %3D Complete the following statements to determine if V is a subspace of R2. (a) V is non-empty If it is non-empty, give two different examples of vectors in V. If it is empty, then leave the following spaces blank. example 1: a = example 2: b = Note: Normally, only one example is required to show V is not empty in a proof. (b) V is ? If it is not closed, enter two vectors a, b e V below, whose sum is not in V. If it is closed, then leave the following spaces blank. + under vector addition. a = b = (c) V is ? + under scalar multiplication. If it is not closed, enter a scalar k and a vector c E V below, whose product is not in V. If it is closed, then leave the following spaces blank. k = and c =

= {(x, y) E R´ | x = y}U{(x, y) E R² |x = -2y}. %3D Complete the following statements to determine if V is a subspace of R2. (a) V is non-empty If it is non-empty, give two different examples of vectors in V. If it is empty, then leave the following spaces blank. example 1: a = example 2: b = Note: Normally, only one example is required to show V is not empty in a proof. (b) V is ? If it is not closed, enter two vectors a, b e V below, whose sum is not in V. If it is closed, then leave the following spaces blank. + under vector addition. a = b = (c) V is ? + under scalar multiplication. If it is not closed, enter a scalar k and a vector c E V below, whose product is not in V. If it is closed, then leave the following spaces blank. k = and c =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determining Subspaces

V = {(x, y) E R² | x = y} u {(x, y) E R² |x = = -2y}. Complete the following statements to determine if V is a subspace of R. (a) V is non-empty If it is non-empty, give two different examples of vectors in V. If it is empty, then leave the following spaces blank. example 1: a = example 2: b = Note: Normally, only one example is required to show V is not empty in a proof. (b) V is ? under vector addition. If it is not closed, enter two vectors a, b e V below, whose sum is not in V. If it is closed, then leave the following spaces blank. a = ( b = (c) V is ? + under scalar multiplication. If it is not closed, enter a scalar k and a vector c E V below, whose product is not in V. If it is closed, then leave the following spaces blank. k = and c = II
Transcribed Image Text:V = {(x, y) E R² | x = y} u {(x, y) E R² |x = = -2y}. Complete the following statements to determine if V is a subspace of R. (a) V is non-empty If it is non-empty, give two different examples of vectors in V. If it is empty, then leave the following spaces blank. example 1: a = example 2: b = Note: Normally, only one example is required to show V is not empty in a proof. (b) V is ? under vector addition. If it is not closed, enter two vectors a, b e V below, whose sum is not in V. If it is closed, then leave the following spaces blank. a = ( b = (c) V is ? + under scalar multiplication. If it is not closed, enter a scalar k and a vector c E V below, whose product is not in V. If it is closed, then leave the following spaces blank. k = and c = II
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